





import sys




def      a__			(       lowercase__	):






   '''simple docstring'''






   UpperCAmelCase_           =len(lowercase__	)
   UpperCAmelCase_           =[[0 for x in range(lowercase__	)] for x in range(lowercase__	)]
   UpperCAmelCase_           =[[0 for x in range(lowercase__	)] for x in range(lowercase__	)]

   for chain_length in range(2	,     lowercase__	):
      for a in range(1	,     n - chain_length + 1	):
         UpperCAmelCase_           =a + chain_length - 1

         UpperCAmelCase_           =sys.maxsize
         for c in range(lowercase__	,     lowercase__	):
            UpperCAmelCase_           =(
                matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
            )
            if cost < matrix[a][b]:
               UpperCAmelCase_           =cost
               UpperCAmelCase_           =c
   return matrix, sol




def      a__			(       lowercase__	,     lowercase__	,     lowercase__	):






   '''simple docstring'''






   if i == j:
      print("A" + str(lowercase__	)	,     end=" "	)
   else:
      print("("	,     end=" "	)
      print_optiomal_solution(lowercase__	,     lowercase__	,     optimal_solution[i][j]	)
      print_optiomal_solution(lowercase__	,     optimal_solution[i][j] + 1	,     lowercase__	)
      print(")"	,     end=" "	)




def      a__			(       ):






   '''simple docstring'''






   UpperCAmelCase_           =[3_0, 3_5, 1_5, 5, 1_0, 2_0, 2_5]
   UpperCAmelCase_           =len(lowercase__	)
   # Size of matrix created from above array will be
   # 30*35 35*15 15*5 5*10 10*20 20*25
   UpperCAmelCase_    ,							UpperCAmelCase_           =matrix_chain_order(lowercase__	)

   print("No. of Operation required: " + str(matrix[1][n - 1]	)	)
   print_optiomal_solution(lowercase__	,     1	,     n - 1	)


if __name__ == "__main__":
     main()












"""simple docstring"""


from math import sqrt


def        UpperCAmelCase      (					a__ = 1_00_00_00 ):





						'''simple docstring'''






						lowerCAmelCase   :int						=			0
						lowerCAmelCase   :int						=			0
						lowerCAmelCase   :int

						while num_cuboids <= limit:
												max_cuboid_size += 1
												for sum_shortest_sides in range(2     ,      2 * max_cuboid_size + 1 ):
																		if sqrt(sum_shortest_sides**2 + max_cuboid_size**2 ).is_integer():
																								num_cuboids += (
																								    min(a__     ,      sum_shortest_sides // 2 )
																								    - max(1     ,      sum_shortest_sides - max_cuboid_size )
																								    + 1
																								)

						return max_cuboid_size


if __name__ == "__main__":
		print(F"""{solution() = }""")